Some connections between dynamical systems and neural networks

Series #VeronesiTuttiMathSeminars #SafetyThenEnjoyMath

Neural networks have been proven to effectively solve problems coming from very different applications. Therefore, in recent years there has been an increasing interest in getting a mathematical understanding of why they work and how they can be exploited to solve some mathematical problem. This talk goes through some connections between dynamical systems and neural networks. We first see how dynamical systems, and their numerical discretizations, can give an interpretation of modern Residual Neural Networks with the consequence of also being able to impose some structure on the network. Finally, we go through an application of neural networks to Hamiltonian systems. In particular, we show how starting from a set of trajectories of a Hamiltonian system, we can accurately approximate the Hamiltonian behind the system thanks to a scalar-valued neural network. This approximation can then be used to generate new trajectories for different initial conditions.

Davide is a second-year PhD student in the group of Differential Equations and Numerical Analysis (DNA) at NTNU, Trondheim, Norway. His PhD project focuses on neural networks and how they interplay with the areas of dynamical systems and differential geometry.

The zoom link to the seminar is https://univr.zoom.us/j/97604696910 and the password is given by the first eight digits of arccos(-1). In order to be informed about the next seminars, please join the following mailing-list

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Marco Caliari

Matteo Frigo, Chairman of Associazione Alumni Matematica Verona